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Large scale electricity storage is set to play an increasingly important role in the management of future energy networks. A major aspect of the economics of such projects is captured in arbitrage, i.e. buying electricity when it is cheap…
We revisit the classical Merton consumption--investment problem when risky-asset returns are modeled by stochastic differential equations interpreted through a general $\alpha$-integral, interpolating between It\^{o}, Stratonovich, and…
Empirical studies indicate the presence of multi-scales in the volatility of underlying assets: a fast-scale on the order of days and a slow-scale on the order of months. In our previous works, we have studied the portfolio optimization…
We consider the problem of maximising expected utility from terminal wealth in a semimartingale setting, where the semimartingale is written as a sum of a time-changed Brownian motion and a finite variation process. To solve this problem,…
In this paper, we study a stochastic optimal control problem with stochastic volatility. We prove the sufficient and necessary maximum principle for the proposed problem. Then we apply the results to solve an investment, consumption and…
We consider the mean-variance hedging problem under partial information in the case where the flow of observable events does not contain the full information on the underlying asset price process. We introduce a martingale equation of a new…
We consider assortment optimization over a continuous spectrum of products represented by the unit interval, where the seller's problem consists of determining the optimal subset of products to offer to potential customers. To describe the…
In this paper we formulate and study an optimal switching problem under partial information. In our model the agent/manager/investor attempts to maximize the expected reward by switching between different states/investments. However, he is…
In this paper we investigate the pricing problem of a pure endowment contract when the insurer has a limited information on the mortality intensity of the policyholder. The payoff of this kind of policies depends on the residual life time…
This paper addresses the problem of utility maximization under uncertain parameters. In contrast with the classical approach, where the parameters of the model evolve freely within a given range, we constrain them via a penalty function. We…
We prove existence and uniqueness of stochastic equilibria in a class of incomplete continuous-time financial environments where the market participants are exponential utility maximizers with heterogeneous risk-aversion coefficients and…
This paper applies computational techniques of convex stochastic optimization to optimal operation and valuation of electricity storages in the face of uncertain electricity prices. Our valuations are based on the indifference pricing…
We give explicit solutions for utility maximization of terminal wealth problem $u(X_T)$ in the presence of Knightian uncertainty in continuous time $[0,T]$ in a complete market. We assume there is uncertainty on both drift and volatility of…
The problem of determining the European-style option price in the incomplete market has been examined within the framework of stochastic optimization. An analytic method based on the discrete dynamic programming equation (Bellman equation)…
We consider the Brownian market model and the problem of expected utility maximization of terminal wealth. We, specifically, examine the problem of maximizing the utility of terminal wealth under the presence of transaction costs of a…
We pursue an inverse approach to utility theory and consumption & investment problems. Instead of specifying an agent's utility function and deriving her actions, we assume we observe her actions (i.e. her consumption and investment…
We consider the estimation of the multi-period optimal portfolio obtained by maximizing an exponential utility. Employing Jeffreys' non-informative prior and the conjugate informative prior, we derive stochastic representations for the…
We study the optimal portfolio liquidation problem over a finite horizon in a limit order book with bid-ask spread and temporary market price impact penalizing speedy execution trades. We use a continuous-time modeling framework, but in…
We investigate the portfolio selection problem for an agent with rank-dependent utility in an incomplete financial market. For a constant-coefficient market and CRRA utilities, we characterize the deterministic strict equilibrium…
This paper studies the continuous time utility maximization problem on consumption with addictive habit formation in incomplete semimartingale markets. Introducing the set of auxiliary state processes and the modified dual space, we embed…